T = c + cb
T = (975) + (975)(0.06) *6% = 0.06
T = 975 + 58.5
T = 1033.5
She spent $1033.5. (what hat costs that much lol)
12A+8W > 343 represents the number of minutes the robot filters air A and water W to filter more than 343 liters of air and water.
If the robot filters air for 20 minutes and water for 15 minutes, plugging A as 20 and W as 15, let us check if the equation is true or not.
Checking left side:
12A + 8W = 12(20) +8(15)
240+ 120 = 360
Checking right side: 343
12A+8W > 343
360>343
True.
So the robot meets the first expectation.
Let us check for second equation:
3A+4W < 49
Left side : 3A +4W = 3(20) +4(15) = 60 +60 =120
Right side is 49
comparing left and right side:
3A+4W < 49
120<49
False.
So the robot does not meet the second expectation.
The correct answer would be the first and the last ones.
Answer:
I assume that this is a quadratic equation, something like:
y = -47*x^2 - 24x + (-36)
we can rewrite it as:
y = -47x^2 - 24x - 36
Ok, this is a quadratic equation and we want to find the maximum value.
First, you can notice that the leading coefficient is negative.
This means that the arms of the graph will open downwards.
Then we can conclude that the vertex of the equation is the "higher" point, thus the maximum value will be at the vertex.
Remember that for a general function
y = a*x^2 + b*x + c
the vertex is at:
x = -b/2a
So, in our case:
y = -47x^2 - 24x - 36
The vertex will be at:
x = -(-24)/(2*-47) = -12/47
So we just need to evaluate the function in this to find the maximum value.
Remember that "evaluating" the function in x = -12/47 means that we need to change al the "x" by the number (-12/47)
y = -47*(-12/47)^2 - 24*(-12/47) - 36
y = -32.94
That is the maximum value of the function, -32.94
